The only way to detect an electron is to have some physical interaction with it. So we aren't simply observing the electron's state, we are interferring with it's state.
This is the essence of the Schrodinger's Cat thought experiment in a nutshell. The cat is the electron being measured and opening the box is the process of measuring it. It isn't that we change the cat in a human-perceptible way, e.g. from alive to dead or vice versa, because cat 'aliveness' (vitality?) isn't a
bona fide quantum state. The slit experiment simply exaggerates the effect to make it obvious.
To abstract a little, quantum mechanics simply attempts to describe the interactions between matter, energy, position, and time. The manner in which one measures/observes a quantum state necessarily changes it. I quite like the idea that, if we didn't have eyes we would be sensing by sound. In this case, the speed of sound would define time and distance, despite there being a faster value (which would be unknown/unobservable to us). It probably isn't a good example because the speed of sound isn't constant, but it's the link between senses and measurement that is important.
The interesting applications are comms and computing. This arises from coupled quantum states (entanglement), where two, or more, states depend on each other. For comms, these states appear to depend on their entangled 'other' despite distance and time. This where you go with Einstein and Rosen and their 'hidden variables' explanation... Einstein didn't want to believe there might be a value faster than the speed of light because his theories depended on it, or Bell and his super-determinism.
It is interesting that qubits rely on imaginary numbers, which implies the addition of an extra orthogonal dimension (such as the imaginary plane). This is, of course, required to explain periodic behaviour in the original dimension (e.g. a rotating phasor). Furthermore, the combination of a probability density function (say, a Gaussian) and a wave function (a sinusoid will do) gives rise to a Morlet wavelet that can be used to investigate both the time and frequency components of a physical signal. In some sense, time and frequency are entangled.
It's a fascinating bit of the pie of science, and very near the centre, so it touches many other scientific disciplines. And philosophy.
